TM5101 
                                        
                Continuous-Time Financial Mathematics
                        €ஹᚃࣛගৌਕᅰኪ
              This course provides a  probabilistic 
              way  in  depth  to  establish  no  arbi-
              trage asset pricing theory under sev-
              eral financial markets and contingent 
              claims. We focus on financial inter-
              pretations of mathematical modeling 
              for  risky  asset  dynamics.  Applica-
              tions of Monte Carlo simulations in 
              financial  engineering  will  be  dis-
              cussed  along  with  the  development 
              of  this  course. Beyond classical  fi-
              nancial models, Levy process and its 
              pricing  and  hedging  theory  will  be 
              addressed. 
              Instructor: Chuan-Hsiang Han (ᒵෂୂ)
              Department of Quantitative Finance, NTHU
              Office: 204-2 Innovation Incubator(ԃϓʕː) 
              Office Hours: 1400 – 1700 Tuesday or by appointment
              Phone: 03-5742224
              Email: chhan@mx.nthu.edu.tw
              URL: enter from http://www.qf.nthu.edu.tw/people/teacher.php
              Class Time: W2W3W4  (9:00AM - 12:00AM) 
              Classroom Location: Room 101, Research and Development Bldg  
              (޼೯101)
              Prerequisities:
              Courses equivalent to TM5091 Stochastic Calculus for Finance ( 
              Ito’s calculus)
              Text:  Steven  E.  Shreve,  “Stochastic  Calculus  for  Finance  II: 
              continuous-Time Models,” Springer-Verlag, 2003.
              References: 
                1.   Damien Lamberton and Bernard Lapeyre, “Introduction to
                      Stochastic Calculus Applied to Finance,”Springer, (1 edition) 
                      1996.
                2.   P. Glasserman, Monte Carlo Methods for Financial 
                      Engineering, Springer-Verlag, New York, 2003.
              Continuous-Time Financial Mathematics  - Syllabus Spring 2007
                         TM5101      Continuous-Time Financial Mathematics
                    Course Contents: 
                        1. Stochastic differential equations for finance (the Markov 
                           property,   interest   rate   models,    multi-dimensional 
                           Feynman-Kac theorems, SDE discretization schemes)
                        2.  Pricing some  exotic options (knock-out barrier options, 
                           lookback options, Asian options, control variate method, 
                           dimension reduction PDEs)
                        3. American derivative securities (stopping times, American 
                           put  and  call  options,  free  boundary  problems,  least-
                           squares and duality methods)
                        4.  Change  of numeraire  (numeraire, foreign and  domestic 
                           risk-neutral  measures,  forward  measures,  importance 
                           sampling)
                        5.  Term  structure  models  (affine-yield  models,  Heath-  
                           Jarrow-Morton model, forward LIBOR model)
                        6.  Introduction  to  Levy  processes (Poisson  process,  com-
                           pound  Poisson  process,  jump  processes and their  Inte-
                           grals, stochastic calculus for jump processes, change  of 
                           measure, pricing and hedging a European Call in a Jump 
                           model, PIDE) 
                        7. Topics on Stochastic Volatility: Perturbation methods, Av-
                           eraging effect, Applications to credit risk.
                    Grading: 
                    Assignments 40%, Exams(midterm and final) 40%, Course Project 20%.
                    Continuous-Time Financial Mathematics  - Syllabus Spring 2007